Solved – Probit estimation – insignificant coefficients with a significant difference

I'm a postgraduate economics student but not of the statistically inclined sort 🙂

Im running a regression to estimate the likelihood of a patent being litigated. I have two dummies for the patent owner type; let's call them SmallFirm and LargeFirm. The reference category is individuals.

What I'm actually interested in is if the difference between the coefficients on Large and Small is negative, which would suggest in my particular case that small firms face a higher litigation risk.

I have quite a small sample size and find each coefficient to be insignificant at the 10% level.
However, when I run an test of equality of coefficients in stata (test LargeFirm=SmallFirm) I get that they are significantly different at the 5 % level.

Dummy     |coeff     |std err  |z-stat |P-value|       CI SmallFirm |-.1636389 |.5219826 | -0.31 |0.754  | (-1.186706,    .8594281) LargeFirm |-.7599469 |.533567  | -1.42 |0.154  | (-1.805719,    .2858252)  . test SmallFirm = LargeFirm  ( 1)  [Litigated]SmallFirm - [Litigated]LargeFirm = 0         chi2(  1) =    5.88      Prob > chi2 =    0.0153 

What can I conclude from this?
Can I say that the significant difference does imply that small firms are associated with a higher likelihood of litigation despite the individual dummies being insignificant?

Thanks so much for the help!

I think I got it now! Thanks Andrea: you got me on the right track.
The dummies are insignificant precisely b/c my choice of reference group: neither large or small firms are statistically significantly more likely to be litigated – than individuals-.

this is not what I was interested in anyway.

If I run a regression with the SmallFirm dummy and an Individual dummy making LargeFirm the reference group: surely enough I do find a significant coefficient on SmallFirm!

So thanks!

Insignificant at the 10% level means that the 90%-confidence interval overlaps with zero. A significant difference at the 1% level means that the (larger!) 99% confidence intervals do not overlap. This should not be possible.

The F-test does not test the hypothesis whether two coefficients are of different size. This test tells you that large firms are not small firms. What you are probably looking for is the Wald test. Maybe that’s the problem?

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